10 The Open Petroleum Engineering Journal, 2008, 1, 10-15

1874-8341/08 2008 Bentham Open

Open Access

New Methods for Predicting Productivity and Critical Production Rate of

Horizontal Wells

Hong’en Dou*

RIPED, PetroChina, P.R. China

Abstract: Horizontal well technology is still applied widely in the world. Some researchers and oilfield operators of hori-

zontal wells are still using improper productivity predicting equations and critical production rate calculations. Therefore,

this paper analyzes some productivity forecast equations and critical coning rate calculation procedures for horizontal

wells focusing on Joshi's equation of predicting productivity and Chaperon's equation of calculating critical coning rate

used in reservoir engineering. This paper suggests that effective permeability should be used in calculating horizontal well

productivity and points out an error existing in Joshi's equation. It also evaluates and introduces several equations for

critical production rate. Furthermore, this paper derives two new equations for predicting horizontal well productivity and

a general predictive equation for horizontal well critical coning rate, applying the Mirror Effect Theory. Field applications

show that the relative error between generally accepted methods of prediction are less than 17% and the new calculation

method is more accurate than that of Joshi’s equation. Moreover, using actual oilfield examples, the modified Chaperon's

equation was verified.

INTRODUCTION

Since 1986, the number of horizontal wells has grown

from 30 to tens of thousands, and the prediction of horizontal

well productivity has become very important. At the begin-

ning of 1980s [1, 2] derived some equations to predict hori-

zontal well productivity. In 1986 and 1991 Joshi [3, 4] re-

derived an equation by using the complex potential method.

A term of ln [h/(2rw)] in the nominator of the Joshi equation

is different from that of ln [h/(2 rw)] in the Renard equa-

tion. The difference is only in Renard equation, but no

difference had been proved in the accuracy of the results by

the author of this paper.

Joshi assumed that the fluid flowing through multi-

porous media could be divided into two components of ver-

tical and horizontal flow. In fact, these two parts are mutu-

ally perpendicular and mutually contained. But in the Joshi

equation, this influence was ignored, and therefore its predic-

tion results were not quite accurate.

In the paper, the Joshi equation was corrected by using

average effective permeability, error between oilfield actual

value and the calculated value of the corrected equation re-

duce to 58%. Also, a new equation was derived by the mirror

image theory [6, 7] to precisely predict the productivity of a

horizontal well in a homogeneous formation.

For water coning/cresting of bottom water reservoirs de-

veloped with horizontal wells, the main concern is the reduc-

tion of production. Control of water coning/cresting is a big

technological problem that has been faced by petroleum en-

gineers for a long time. Many researchers have spent a great

deal of energy in studying the calculation method for critical

*Address correspondence to this author at the RIPED, PetroChina, P.R.

China; E-mail: douhongen@petrochina.com.cn or dohe@public.bta.net.cn

production rate [1, 5, 8-12] in horizontal wells for water con-

ing/cresting. However, based on the same production well

data, different equations will give different results, which

can cause great trouble to the petroleum engineers. In the

paper, a new calculation formula for critical production was

introduced.

DISCUSSION OF PRODUCTIVITY EQUATIONS

In 1986 and 1991 Joshi [3, 4] has given several produc-

tivity equations as follows:

Joshi equation

Qh =2 Khh

μBo

P

lna + a2 (L / 2)2

L / 2+h

Lln

h

2rw

(1)

where a = 0.5 0.5 + 0.25 + (1 (L / 2rw ))4( )0.5

Borison equation

Qh =2 Khh

μBo

P

ln4rehL

+h

Lln

h

2 rw

(2)

Giger equation

Qh =2 Khh

μBo

P

ln1+ 1 (L / 2reh )

2

L / 2reh+h

Lln

h

2 rw

(3)

Renard and Dupuy equation

Qh =2 Khh

μBo

P

ln1+ 1 (L / 2a)2

L / 2a+h

Lln

h

2 rw

(4)

It is obvious that the difference between the Joshi equa-

tion and the Renard and Dupuy equation is a constant term

Predicting Productivity and Critical Production Rate of Horizontal Wells The Open Petroleum Engineering Journal, 2008, Volume 1 11

in the nominator of the Joshi equation. In addition, the

only difference between the equations of Giger and Joshi is

Giger assumed a=reh. But the Borison equation thought

a=reh, and when value L/2reh is very little, and it can be ig-

nored, the Renard and Dupuy equations were turned into the

Borison equation; here, what must be mentioned, the equa-

tion (1) to (4) can be suitably applied to isotropic reservoir

formation. However, when the above equations are changed

into reservoir engineering units, 2 can be replaced by

5.425 102

.

DISCUSSION OF THE JOSHI EQUATION

Joshi (1986) [3] assumed that fluid flowing into a hori-

zontal well may be divided into two parts, one is flowing on

a horizontal plane and the other is flowing on the vertical

plane and come to the ellipse drainage in the horizontal plane

and cylindrical drainage in vertical plane. The flow resis-

tance in the two planes was calculated respectively, using a

productivity formula similar in principle with Ohm and

Darcy. It is clear that the Joshi equation should not eliminate

this overlapping factor and thus result in error in the produc-

tivity calculation of horizontal wells.

Using average effective permeability, the productivity

prediction of anisotropy formation is reasonable, and people

still divide permeability into the horizontal and the vertical.

In fact, fluids flowing through porous media in the vertical

and the horizontal planes influence and interact on each other

in the reservoir. The permeability direction in formation will

be disordered and unsystematic because the actual effect in

the reservoir will not be really simulated. The permeability

value is different in the different directions; therefore, fluid

will flow toward the direction that has the low flow resis-

tance. The three permeability of Kx, Ky and Kz were difficult

to acquire. Moreover, by using Muskat’s Z ' = h KhKv

the hori-

zontal well production equation of the isotropic formation

was transformed into anisotropic formation as follows:

Qh =2 Khh

μBo

P

lna + a2 (L / 2)2

L / 2+

h

Lln

h

2rw

(5)

where =Kh

Kv

It is clear that in equation (5), production rate Qh is in-

versely proportional to , and is directly proportional to Kh,

but is associated with Kh and Kv. Only when the value

is very low (0< <1), the Qh value can increase, however,

Qh change is also considerably sensitive to Kh. For equation

(5), when Kh is less than Kv and Kh is much lower, the Qh

value is also lower. In the case, the actual value of Qh from

the oilfield is more than the calculation value. By contrast,

when Kh is more than Kv, and Kh is much bigger, the Qh

value is also bigger; however, the actual value of Qh from

oilfield is not as high as that. In general, when we calculate

Qh, no matter what Kh and Kv are, neither is stable. The paper

suggests replacing the horizontal permeability or vertical

permeability with average effective permeability, as follows:

K = KhKv (6)

Horizontal well productivity calculation applies the equa-

tion (6) is reasonable. Substituting it into equation (5) we

have a corrected Joshi equation:

Qh =2 Kh

μBo

P

lna + a2 (L / 2)2

L / 2+h

Lln

h

2rw

(7)

NEW EQUATION OF PRODUCTIVITY PREDICTION

IN HORIZONTAL WELL

We assume the horizontal well is the same as a straight

vertical well; the horizontal length is equal to the reservoir

thickness. Furthermore, we assume the producer in the infi-

nite formation, and a new productivity equation was derived

by the Mirror Effect Principle [6, 7].

According to the complex potential principle [6], we ob-

tain

=q

2ln r

+

+

+ c (8)

where:

=q

2[ln X 2

+ (Z 2nh Zw )2

+

+

+

ln X 2 (Z 2nh + Zw )2 ]+ c

(9)

=q

4ln ch

X

hcos

(Z Zw )

h, ch

X

hcos

(Z + Zw )

h, + c (10)

Through simplification (see Appendix A):

=q

2

reh

+ lnh

2 rwsin

Zw

h (11)

When a horizontal well was drilled in the reservoir center

without eccentricity, Zw=h/2, the equation (11) was reduced

into:

=q

2

reh

+ lnh

2 rw (12)

Therefore:

=K

μP (13)

Combining equation (12) and (13), we obtain:

q =2 K

μ

Preh

+ lnh

2 rw

(14)

For a horizontal well of length L, production rate Q is

calculated as:

Q = qL =2 K

μ

PreL

+h

Lln

h

2 rw

(15)

Equation (15) represents horizontal well production rate

in infinite formation:

12 The Open Petroleum Engineering Journal, 2008, Volume 1 Hong’en Dou

Q =2 Kh

μBo

PreL

+h

Lln

h

2 rw

(16)

To transform the above equation into actual reservoir

engineering unit (S.I system) equation (16) is expressed as:

Q =5.4295 102Kh

μBo

PreL

+h

Lln

h

2 rw

(17)

COMPARISON OF NEW EQUATION AND THE

JOSHI EQUATION

Three horizontal wells, as exampled in China, are Leng-

ping 3 (L-3) in Liaohe oilfield, Shuping 1 (S-1) in Daqing

oilfield and Renping 1 (R-1) in Huabei I oilfield. The base

data is shown in Table 1.

The procedures for estimating these three wells are:

1. Calculate horizontal well production rate using equa-

tion (17).

2. Estimate well production rate using Joshi’s equation

(5).

3. Estimate well production rate using corrected Joshi’s

equation (7).

4. Compare results of equation (17), (5) and (7).

Actual reservoir data of the three oilfields are shown in

Table 1; several estimated results for horizontal well produc-

tivity are listed in Table 2.

DISCUSSION ON THE FORMULATION OF THE

CRITICAL PRODUCTION RATE OF HORIZONTAL

WELLS

Definition of Critical Production Rate

The concept of critical production rate has always been

used in vertical well production. This concept is expressed

as: “the critical production rate is the maximum oil produc-

tion rate without water or gas” [3, 4]. Although Joshi had

introduced it in the horizontal wells, in practice, many schol-

ars thought that the critical production rate is production rate

of the first water drop to appear on the surface in a bottom

water reservoir. Actually, water had broken through the wa-

ter-oil contact (WOC) before the first water drop appears on

the surface, so this production rate cannot be defined as criti-

cal production. It has been considered [11] that the definition

of critical production rate in a bottom water reservoir may be

defined as the production rate at which the plane of WOC

about starts to deform. The author of the paper thinks that the

definition accords with the actual reservoir development.

Discussion and Correction of Chaperon Formulation

Chaperon’s formulation (1986) [8] was derived by using

the Laplace equation under the postulation of constant pres-

sure boundary. The author found some errors in the Chap-

eron derivation, which will be discussed in detail in the fol-

lowing.

Chaperon Derivation was expressed as

Qc = 3.486 10 5 KhL

μ21 cos

Zsc

h

sinZsc

h

(18)

But Chaperon recommended using

Qc = 3.486 10 5 h( )KhhLF

XAμ (19)

In the equation, when the value of F is 4, which is given

by Chaperon, the greatest calculation error is only 44%.

Later in 1986, Joshi [3] has regressed F, and given a formula

as:

F = 3.9624955 + 0.0616348 0.000548 2 (20)

= (XA

h) Kv

Kh

Below will discuss Chaperon’s formula error and make a

modification to the Chaperon equation.

From the trigonometric function, the following expres-

sion can be obtained:

tgZsc

2h=

1 cos(Zsc

h)

sin( Zsch )

(21)

Table 1. Reservoir Basic Parameters

Well No. L (m) h (m) rw (m) re (m) μ (mPa s) Kh ( )23

10 mμ Kv ( )2310 mμ Pe (MPa) Pw (MPa) Bo

L-3

S-1

R-1

368

309

300

36.5

14.0

6.5

0.12

0.061

0.1094

100

239.4

170

41

3.0

6.2

1.00

1.13

1.08

10.0

1.30

9.50

7.50

0.04

3.00

17.33

17.0

19.5

4.0

4.0

19.2

1.00

1.13

1.083

Table 2. Comparison of the Calculation Value with Oilfield Actual Value

Well No. Qa (t/d) Qn (t/d) Qne (%) Qj (t/d) Qje (%) Qjc (t/d) Qjce (%)

L-3 44.3 43.87 0.97 98.33 121.96 36.18 18.3

S-1 8.88 7.33 17.5 21.24 139.3 14.05 58.2

R-1 89.9 89.66 0.29 16.00 82.20 119.75 33.2

Predicting Productivity and Critical Production Rate of Horizontal Wells The Open Petroleum Engineering Journal, 2008, Volume 1 13

Then, equation (1) can also be expressed as:

Qc = 3.486 10 5 KhL

μ2tg

Zsc

2h (22)

When Zsc is approaching zero, Qc will approach zero; Zsc

approaches h, Qc will be infinite. From the above discussion

we can see that the critical production will be infinite when

the coning height is h. Obviously, this is impossible.

The error is caused by the use of a dimensionless critical

production rate equation:

q* = 21 sin Zsc h( )cos Zsc / h

(23)

In 1990, Dikken [12] had shown the error of Chaperon’s

equation, but there is no detailed derivation in his paper.

By using the Chaperon equation, the calculated critical

rate is bigger than that from other equations. This basic

equation was given by Chaperon:

P =Qμ

2 LKln(ch

XA

hcos

Zw

h) (24)

Bottom water reservoir does not happen to coning/cres-

ting under condition:

P g(h Zw ) (25)

The following equation can be derived from equation

(24) and (25)

Qcv = 5.317Kh

μBo

h(1 Zw h)h

Lln ch

XA

hcos

Zw

h

(26)

Now, let us discuss the correction to the formula. When h

approaches Zw, the production is zero. This is right because

of water breakthrough into wellbore.

Example and Discussion

Let us take the No. 3 horizontal well in Tazhong of

Tarim oilfield in China (the well is TZ4-27-H14), as an ex-

ample, the reservoir data of this well are listed in Table 3.

Using data in Table 1, the following represents the results

from equation (19) and (26) respectively: Qc =512.99 m3/d

and Qcv =143.05 m3/d. The critical production calculation

value of the Chaperon equation is 3.58 times larger than the

corrected equation value. The reason leading to this error is

that Chaperon and Joshi did not determine the critical height

and assumed it only by experience value. Unfortunately, this

experience value is quite deviation from the actual results.

Giger’s Formula

In 1986, IFP (Institut Francais du Petrole), Giger (1986)

[9] derived a formula to calculate the critical production of

horizontal wells with bottom water coning/cresting, on the

basis of the postulation, the three sides are closed and im-

permeable. It is expressed as follows:

Qc = 1.251 10 3 KhXA

μBo1+16

3(h

XA

)21/2

1 L (27)

The result was obtained from equation (27) using the data

in Table 3.

Qc=785 m3/d

Table 3. Reservoir Parameters of Well TZ4-27-H14

Surface oil density s

0.84 g/cm3

Underground water density w

1.06 g/cm3

Underground oil density o

0.65 g/cm3

Oil volume factor Bo

1.615 m3/m3

Producing pressure drop P 1.26 MPa

Viscosity of underground oil μ 0.29 m Pa.s

Horizontal permeability Kh 0.164μm2

Vertical permeability Kv 0.0492μm2

Diameter of wellbore rw 0.11 m

Diameter of drainage re 300 m

Thickness of reservoir h 33.5 m

Length of horizontal section L 444.4 m

Distance from bottom of oil layer Zw 22.75 m

Actual oil production rate Qa 1056 t/d

Eccentricity distance of horizontal well 0.6 m

Therefore, this equation is seldom used in petroleum en-

gineering because it is too small and is subject to large er-

rors. This error is caused by the incorrect coning shape func-

tion which can not depict the actual water cresting shape.

Joshi’s Formula

In 1986, based on Muskat’s vertical well critical produc-

tion formula, Joshi derived his horizontal well critical pro-

duction formula:

Qc = qovln(re rw )

ln(re rw' )

h2 (h Ih )2

h2 (h Iv )2 (28)

where:

qov =2.625 10 3 Kh[h

2 (h Iv )2 ]

μB ln(re rw' )

(29)

rw'=

rehL

2a 1+ 1 (L / 2a)2 (h / 2rw)h / L

The following equation is obtained by combining equa-

tions (28) and (29):

Qc =2.625 10 3 Kh[h

2 (h Ih )2 ]

μBo ln1+ 1 (L / 2a)2

L / 2a+h

Lln

h

2rw

(30)

14 The Open Petroleum Engineering Journal, 2008, Volume 1 Hong’en Dou

Below is the corresponding critical production rate ob-

tained by inputting data from Table 3 into equation (30): Qc

=42 m3/d. Obviously, equation (30) is derived by replacing

the pressure differential ( P ) in the stationary solution

equation with the critical condition ])([ 22

hIhhP ,

which was used by Muskat in his derivation of critical pro-

duction for the vertical wells.

NEW METHOD OF THE CRITICAL PRODUCTION

RATE CALCULATION

When crude oil was produced from the bottom water

reservoir, in the well producing process, water moves up

toward the breakthrough into the wellbore in a coning shape

after production pressure difference exceeds a certain pres-

sure. In those cases, water will break through into the oil

well and oil and water are produced together. Our research

purpose is to ensure the WOC does not deform in horizontal

wells. In other words, how do we determine the critical pro-

duction rate of horizontal wells? We also hope to know, the

critical production rate in which there is no water production

at any time. What is the condition without water coning? We

will show one as follows:

P = 9.8 10 3( w o )Zw (31)

Equation (32) is derived on the basis of reference 6:

Qc =5.4259 102Kh[9.8 10 3( w o )]Zw

μBoreL

+h

Lln

h

2 rwcos

h

(32)

Re-writing equation (31), as the following:

Qc =5.4259 102Kh P

μBoreL

+h

Lln

h

2 rwcos

h

9.8 10 3( w o )Zw

P

(33)

where:

Qh =5.4259 102Kh P

μBoreL

+h

Lln

h

2 rwcos

h

Therefore:

Jh = Qh P (34)

Equation (32) can also be rewritten, as:

Qc = 9.8 10 3( w o )ZwJh (35)

The critical production is Qc=177 m3/d by inputting data

from Table 3 into equation (33) or (35). The relative error of

this result is 19.2% compared with Chaperon’s corrected

equation.

In all cases, the Chaperon, Giger and Joshi equations

used to predict the critical production rate result in different

results. The result of Chaperon’s predicting is highest

amongst these three equations. In general, for the well Taz-

hong 4 of Tarim oilfield in China (the well is TZ4-27-H14),

if the Chaperon equation was recommended to use in the

reservoirs, water will break through into well in a short time,

and thus using Chaperon’s equation to predict critical pro-

duction rate is improper. Therefore, it is recommended to use

the new method that is close to the actual data of the oilfield

for critical production rate predicting.

CONCLUSIONS

1. The errors between calculation result of the Joshi

equation and oilfield actual result range from 82.2%

to 121.96% when Joshi’s equation was used to predict

horizontal well productivity in well L-3, S-1 and R-1.

the errors between predicting results of corrected

Joshi equation and oilfield actual results were de-

creased, ranging from 18.3% to 58.2%, therefore, the

corrected equation can also be used to predict hori-

zontal well productivity.

2. The new productivity predicting equation is not only

simple but also has high predicting accuracy when its

calculation results compared with the oilfield actual

results, with the largest relative error is 17.5%.

3. The original derivation of Chaperon’s critical produc-

tion rate equation is correct, but there are errors in the

simplified equation, which has been modified by the

author in the paper.

4. The author suggests that the new critical production

rate equation and the modified Chaperon equation

both were recommended to determine the critical

production rate for horizontal wells with bottom wa-

ter reservoirs because its relative error is only 19.2%

by comparison of critical production rate between the

calculation result of new equation with the modified

Chaperon’s equation.

NOMENCLATURE

K = Effective permeability, μm

2

KVv =

Vertical permeability, μm2

Kh = Horizontal permeability, μm2

μo

= Underground oil viscosity, mPa•s

L = Length of horizontal well, m

rw = Radius of well bore, m

reh

= Drainage radius of horizontal well, m

h = Thickness of oil reservoir, m

Bo = Oil volume factor

re = Drainage radius, m

q* = Dimensionless critical production rate

= Middle constant

= Formation anisotropic coefficient, dimensionless

w = Underground water density, g/cm

3

o = Underground oil density, g/cm

3

= Difference of underground water and oil density,

g/cm3

Zsc = Coning height of bottom water, m

XA = Drainage radius of vertical toward horizontal well

length, m

Predicting Productivity and Critical Production Rate of Horizontal Wells The Open Petroleum Engineering Journal, 2008, Volume 1 15

= Eccentricity distance of horizontal well, m

Zw = Distance from bottom of oil layer to horizontal well,

m

= Fluid potential

F = Dimensionless function

Qh = Production well of horizontal well, m3/d

Qc = Critical production rate, m3/d

Qcv = Critical production rate calculated by corrected

Chaperon’s Equation, m3/d

Iv = The distance between the oil-water contact and the

top of perforated section in the vertical well, m

Ih = Distance between horizontal well and the water-oil

or oil- gas interface, m

reh = Radius of drainage oil, m

Qa = Value of actual production, m3/d (tons/day=t/d)

Qn = Calculation value from equation (17) m3/d

(tons/day)

Qne = Error of equation (17) versus Qa, %

Qj = Calculation value of Joshi’s equation (5), m3/d

(tons/day)

Qje = Error of Joshi’s equation (5) versus Qa, %

Qjc = Calculation value of equation (7), m3/d (tons/day)

Qjce = Error of equation (7) versus Qa, %

Pe = Formation pressure, MPa

Pw = Flow pressure in the horizontal well, MPa.

P = Producing pressure drop, MPa

APPENDIX A: POTENTIAL DIFFERENTIAL OF

BOTTOM-HOLE

According to below potential function

=q

4ln ch

X

hcos

(Z Zw )

hch

X

hcos

(Z + Zw )

h+ c (1a)

When Z=Zw, X=rw, in terms of equation (1a), potential

distribution at bottom hole was expressed as follows

w =q

4ln ch

rwh

1 chrwh

cos2 Zw

h+ c (2a)

When rw << h equation (2a) was simplified as fol-

lows

w =q

2ln

rwhsin

Zw

h+ c (3a)

When Z=Zw, X=re, and when

ch X h >> 1 ch ( X h) 1 ch( X h)

ch( X h) cos (2 Zw h) ch X h

Potential distribution at drainage boundary of reservoir

was expressed as follows

e =q

2ln ch

reh

+ c (4a)

Therefore, potential difference at bottom hole of horizon-

tal well

= e w =q

2ln

ch re hrwhsin

Zw

h

+ c (5a)

When re >>h

ch ( re h) = (1 2)eZw h

Equation (5a) was further simplified, and potential dif-

ferential at horizontal well bottom hole was obtained as fol-

lows:

=q

2

reh

+ lnh

2 rwsin

Zw

h

REFERENCES

[1] F. M. Giger, L. H. Reiss, A. P. Jourdan, “The Reservoir Engineer-

ing Aspects of Horizontal Drillling, SPE13024,’’ presented at SPE Annual Technical Conference and Exhibition, Houston, USA,

1984. [2] G. L. Renard, and J. M. Duppuy, “Influence of Formation Damage

on the Flow Efficiency of Horizontal wells, SPE19414,” Formation Damage Control Symposium, Lafayette, Louisiana, February,

1990. [3] S. D. Joshi, “Augmentation of Well Productivity With Slant and

Horizontal Wells, SPE15375,’’ presented at SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 5-8 October,

1986. [4] S. D. Joshi, “Horizontal Well Technology”. Penn Well Publishing

Company; Tulsa, OK, 1991. [5] B. J. Karcher, F. M. Giger, J. Combe, “Some Practical Formations

to Predict Horizontal Well Behavior; SPE 15430,” presented at SPE Annual Technical Conference and Exhibition, New Orleans,

Louisiana, USA, 1986. [6] M. Muskat, “The Flow of Homogeneous Fluids through Porous

Media”, International Human Resouces Development Corporation, Boston, USA, 1982, pp. 175-191.

[7] J. Bear, “Hydraulics of Groundwater, Mcgraw-Hill Series in Water Resources and Enviromental Engineering”, New York: Mcgraw-

Hill Inc. 1979, 356-367. [8] I. Chaperon, “Theoretical Study of Coning Toward Horizontal and

Vertical Wells in Anisotropic Formations: Subcritical and Critical Rates, SPE15377,” presented at SPE Annual Technical Conference

and Exhibition, 5-8 October, New Orleans, Louisiana, USA, 1986. [9] F. M. Giger, “Analytic 2-D Models of Water Cresting Before

Breakthrough for Horizontal Wells; SPE15378,” presented at SPE Annual Technical Conference and Exhibition, New Orleans, Lou-

isiana, USA, 1986. [10] Boyong Guo, R. L. Lee, “Determination of the Maximum Water-

Free Production Rate of a Horizontal Well with Water/Oil Inter-face Cresting; SPE24324,” presented at SPE Rocky Mountain Re-

gional Meeting, 18-21 May, 1992, Casper, Wyoming. [11] P. Permadi, “Practical Methods to Forecast Production of Hori-

zontal Wells; SPE29310,” presented at SPE Asia Pacific Oil and Gas Conference, Kuala Lumpur, Malaysia, 1995.

[12] B. J. Dikken, “Pressure Drop in Horizontal wells and Its Effect on Production Performance,” Journal of Petroleum Technology, pp.

1426-1433, November 1990.

Received: January 30, 2008 Revised: February 27, 2008 Accepted: March 31, 2008

© Hong’en Dou; Licensee Bentham Open.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/license/by/2.5/), which permits unrestrictive use, distribution, and reproduction in any medium, provided the original work is properly cited.